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Componendo and Dividendo

From the sum ...

Question

From the sum of $7 - 2 x$ and $5 + 4 x - 5 x^{3}$ , subtract the sum of $4 x^{3} - 7 x$ and $- x^{3} - x + 1$ .

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Solution

Step 1: Finding the required sum of the algebraic expression
First, adding $7 - 2 x$ and $5 + 4 x - 5 x^{3}$
$7 - 2 x + (5 + 4 x - 5 x^{3}) = 7 - 2 x + 5 + 4 x - 5 x^{3} = - 5 x^{3} + 2 x + 12 . . . (i)$
Now, finding the sum of $4 x^{3} - 7 x$ and $- x^{3} - x + 1$
$4 x^{3} - 7 x + (- x^{3} - x + 1) = 4 x^{3} - 7 x - x^{3} - x + 1 = 3 x^{3} - 8 x + 1 . . . (i i)$
Step 2: Finding the difference in an algebraic expression
Now, subtracting eqn(ii) from eqn(i), we get
$- 5 x^{3} + 2 x + 12 - (3 x^{3} - 8 x + 1) = - 5 x^{3} + 2 x + 12 - 3 x^{3} + 8 x - 1 = - 8 x^{3} + 10 x + 11$
Hence, the final answer is $- 8 x^{3} + 10 x + 11$

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Similar questions

Q. Subtract the sum of

2 x^{2} - 4 x + 11

7 x^{2} - 4 x + 1

from the sum of

8 x^{2} - 7 x - 7

6 x^{2} + 4 x - 6.

Q. From the sum of

4 + 3 x

5 - 4 x + 2 x^{2}

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3 x^{3} - 5 x

- x^{2} + 2 x + 5

Q. What must be added to 5x³ − 2x² + 6x + 7 to make the sum x³ + 3x² − x + 1?
(a) 4x³ − 5x² + 7x + 6
(b) −4x³ + 5x² − 7x − 6
(c) 4x³ + 5x² − 7x + 6
(d) none of these

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. What is the final result?

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